Module 5FA Review

1. What are the 4 conic sections?

2. Conic sections are generated from a ______intersecting a ______.

( x+3)2( y + 2) 2 3. Given the equation + = 1, where is the center of the conic section? 4 4

4. Which of the conic sections can be a function?

5. Which way does the parabola, y= -1( x + 3)2 - 4 , open?

6. The asymptotes of a hyperbola are….

( x+3)2( y + 2) 2 7. What conic section is represented by the equation, + =1 ? 4 4

8. Which conic section has only one focus?

9. Which conic section has a directrix?

10. Write the equation of the circle illustrated above. (Assume that each line represents 1 unit and that the radius is a whole number.)

11. Name the center and the radius of the circle represented by the equation x2+( y + 2) 2 = 9 . Be sure to give 2 answers, the coordinate of the center and the value of the radius. x2 y 2 12. The major axis for the ellipse with the equation + =1, will 16 49 be______(vertical or horizontal)

13. What are the coordinates of the foci for the equation in number 12? Give your answers as ordered pairs.

14. Write the equation of the ellipse illustrated above. (Assume that each line represents 1 unit and the x and y intercepts are integers.)

15. Write the equation of the ellipse with foci at (+/-2,0) and x-intercepts at +/-5.

16. Write the equation of the parabola with focus at (0,4) and directrix y = -4.

17. Find the axis of symmetry, the focus, and the equation for the directrix for the 1 parabola … x= y2 28 Also make sure you know what the variables a and c stand for in a parabola.

18. Please review 5.10 A. You will be asked to find the intercepts, foci and asymptotes of a hyperbola if given a equation. B. You will be asked to write the formula of a hyperbola when given a graph. C. You will be asked to give the slope of both the transverse and conjugate axes from the equation of a hyperbola.

19. If you are given the equation of an ellipse, be able to identify the: x and y intercepts, the length of the major axis, the direction, and the coordinates of the foci. 20. Given the x and/or y intercepts, be able to write the equation of a circle.

21. Which way does the parabola x= -2 y2 open?

Answers:

1. circle, ellipse, parabola, hyperbola 2. plane, cone 3. (-3,-2) 4. Review Parabolas, Circles, ellipses, and hyperbolas (Hint: vertical line test) 5. down 6. Extending the diagonals of this rectangle creates the asymptotes of the hyperbola. The hyperbola approaches these lines but never meets them. 7. circle 8. parabola 9. parabola 2 2 10. x +y = 9 11. r=3 center (0,-2) 12. vertical 13. (0, 33 ) x2 y 2 14. + = 1 25 4 x2 y 2 15. + = 1 25 21 1 y = x2 16. 16 17. axis of symmetry: y = 0 , focus (7,0) directrix: x = -7 18. review lesson 5.10 19. review lesson 5.05 20. review 5.02a and 5.03a 21. opens left